Timeline for What does the action of a 2-torsion line bundle on $Pic^d(C)$ do to the number of sections?
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| S Nov 28, 2015 at 22:16 | history | bounty ended | CommunityBot | ||
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| S Nov 20, 2015 at 20:41 | history | bounty started | gradstudent | ||
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| Nov 20, 2015 at 20:39 | history | edited | gradstudent | CC BY-SA 3.0 |
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| S Nov 10, 2015 at 15:55 | history | bounty ended | CommunityBot | ||
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| Nov 4, 2015 at 17:17 | comment | added | meh | Unless I misunderstand your notation $W_0^d = {A \mbox{ s.t. } h^0(A) \geq 1 } = {C_d)} $ and the expected dimension is d . In addition, plugging r=0 into the formula $g -(g-d+r)(r+1) gives the Brill-Noether number of effective line bundles is d, which is to be 'expected'. | |
| Nov 4, 2015 at 14:49 | comment | added | gradstudent | @aginensky, Oh then what is the expected dimension? | |
| Nov 4, 2015 at 14:08 | comment | added | meh | One statement in the question is wrong $W^0_d$ has expected (and actual) dimension d. | |
| Nov 2, 2015 at 15:55 | history | edited | gradstudent | CC BY-SA 3.0 |
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| Nov 2, 2015 at 15:35 | history | edited | gradstudent | CC BY-SA 3.0 |
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| Nov 2, 2015 at 15:30 | history | edited | gradstudent | CC BY-SA 3.0 |
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| Nov 2, 2015 at 15:28 | answer | added | Felipe Voloch | timeline score: 2 | |
| S Nov 2, 2015 at 14:32 | history | bounty started | gradstudent | ||
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| Nov 2, 2015 at 14:31 | history | edited | gradstudent | CC BY-SA 3.0 |
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| Oct 2, 2015 at 15:44 | comment | added | roy smith | Have you heard of Prym differentials? They are sections of the tensor product of the canonical bundle with a 2 torsion line bundle. This 2 torsion bundle determines a double cover D of the curve C, and the Prym differentials on C correspond to differentials on D that are skew symmetric for the sheet exchange involution of D. Maybe that pattern generalizes. (Oh and there are always only g-1 indept Prym diferentials on a curve of genus g.) | |
| Oct 2, 2015 at 15:41 | comment | added | gradstudent | Thanks @abx, if we consider $W^{g-2}_{2g-2}\setminus W^{g-1}_{2g-2}$ this will be preserved by tensor product by a order 2 line bundle. That's why I had this doubt. How do we prove your claim? Can you give me any leads? | |
| Oct 2, 2015 at 6:05 | comment | added | abx | Certainly not. Take for $C$ a hyperelliptic curve: then $W^1_2$ has only one point, which is not preserved by tensor product with any line bundle of order 2. In fact, I believe the situation you describe never happens when $\dim W^r_d<g$. | |
| Oct 2, 2015 at 3:02 | history | asked | gradstudent | CC BY-SA 3.0 |